The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  1  1  X  X  1  X  X  1  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0 2X  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0
 0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0  0
 0  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0  0
 0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0  0  0

generates a code of length 66 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+15x^64+222x^66+15x^68+2x^82+1x^100

The gray image is a code over GF(2) with n=528, k=8 and d=256.
This code was found by Heurico 1.16 in 0.156 seconds.